6.1 The Standard Normal Distribution 1. Fill in the blanks using both our textbook and Lumen textbook. 2. A normal distribution is a continuous probability density function used to model the probability distribution of a random variable. The functions of all normal distributions are already defined: f(x) = So, every normal distribution is completely determined by the two parameters . and ., which are called the mean and the standard deviation. 3. If X ~ N(3, 1), then P(X = 4) = 0 and P(X < 4) = P(X < 4) because every normal distribution function is a probability density function of a continuous random variable. 4. When X ~ N(µ,0), a probability P(a < X < b) is given as the area between the graph and the x-axis over [a,b]. 5. One way of using normal distribution modeling: For a random variable whose mean and standard deviation are known, we assume that the random variable fits the normal distribution with the same mean and standard deviation. Then, we use the normal distribution to find the probabilities of the variable. 6. Notation. X ~ N(µ,0) means that

Continuous random variables 6. A charity group raises funds by collecting waste paper. A skip-full will contain an amount, X of other materials such as plastic bags and rubber bands. X may be regarded as a random varibales with probability density funnction. All nmerical values are in units of 100kg. Find the Expected value and Standard deviation.Express your answer in 3 decimal place value f(x)= - c(x-1)(4-x) 0 for 1